Question

If The Plane Mirror Is Rotated Through An Theta Then The Reflected Ray Turns Through An Angle Of 2 Theta Prove It

Answer 1

when the mirror is tilted at an angle θ, the incident ray will fall on the mirror making an angle of 2θ with normal. as the incidnet angle is 2θ , the angle of relection will also be 2θ . refer the attachment for diagram

Answer 2

Angle of Reflection increases by $\bold{2\theta}$  if plane mirror is rotated through an angle $\bold{\theta}$

Solution:  

The plane mirror when incident with ray of light at an angle, it reflects the ray at the same angle. But when the mirror is rotated by an angle of theta, ray reflected will have twice the angle as 2 theta, because of the following reason,

As we know, Angle of incidence = Angle of reflection

Assume Angle of incidence=Angle $\gamma$=Angle of reflection

Therefore when plane mirror is rotated by θ angle, the normal is moved by \theta angle and angle of incidence, so angle of incidence 2 will now becomes –

Angle of incidence 2=Angle $\gamma+\theta$

So, Angle of reflection will now be –

Angle of reflection 2=Angle $\theta+(\gamma+ \theta)$

Angle of reflection 2=Angle $2\theta+ \gamma$

Therefore, Angle of reflection increases by $\bold{2\theta}$.